We argue that one of the following statements must be true: (a) extensive violations of quantum information theory's additivity conjectures exist or (b) there exists a set of `disentangled' black hole microstates that can account for the entire Bekenstein-Hawking entropy, up to at most a subleading $O(1)$ correction. Possibility (a) would be a significant result in quantum communication theory, demonstrating that entanglement can enhance the ability to transmit information much more than has currently been established. Option (b) would provide new insight into the microphysics of black holes. In particular, the disentangled microstates would have to have nontrivial structure at or outside the black hole horizon, assuming the validity of the quantum extremal surface prescription for calculating entanglement entropy in AdS/CFT.
Typical black hole microstates in AdS/CFT were recently conjectured to have a geometrical dual with a smooth horizon and a portion of a second asymptotic region. I consider the application of the holographic complexity conjectures to this geometry. The holographic calculation leads to divergent values for the complexity; I argue that this classical divergence is consistent with expectations for typical microstates.
Recently, it was proposed that there must be either large violation of the additivity conjecture or a set of disentangled states of the black hole in the AdS/CFT correspondence. In this paper, we study the additivity conjecture for quantum states of fields around the Schwarzschild black hole. In the eternal Schwarzschild spacetime, the entanglement entropy of the Hawking radiation is calculated assuming that the vacuum state is the Hartle-Hawking vacuum. In the additivity conjecture, we need to consider the state which gives minimal output entropy of a quantum channel. The Hartle-Hawking vacuu…
From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on $T^6$, represented by four stacks of D-branes wrapped on various cycles …
The black hole information paradox is one of the most important issues in theoretical physics. We review some recent progress using string theory in understanding the nature of black hole microstates. For all cases where these microstates have been constructed, one finds that they are horizon sized `fuzzballs'. Most computations are for extremal states, but recently one has been able to study a special family of non-extremal microstates, and see `information carrying radiation' emerge from these gravity solutions. We discuss how the fuzzball picture can resolve the information paradox. We use …
We quantize the moduli space of regular D1-D5 microstates, directly from Type IIB SUGRA. The moduli space is parametrized by a smooth closed non-selfintersecting curve in four dimensions, and we derive that the components of the curve satisfy chiral boson commutation relations, with the correct value of the effective Planck constant previously conjectured using U-duality. We use the Crnkovic-Witten-Zuckerman covariant quantization method, previously used to quantize the `bubbling AdS' geometries, combined with a certain new `consistency condition' which allows us to reduce the computation to q…
The construction of neutral black hole microstates is an important problem, with implications for the information paradox. In this paper we conjecture a construction of non-supersymmetric supergravity solutions describing D-brane configurations which carry mass and angular momentum, but no other conserved charges. We first study a classical string solution which locally carries dipole winding and momentum charges in two compact directions, but globally carries no net winding or momentum charge. We investigate its backreaction in the D1-D5 duality frame, where this object becomes a supertube wh…
We study microstates of the three dimensional black hole obtained by quantizing topologically non-trivial geometries behind the event horizon. In chiral gravity these states are found by quantizing the moduli space of bordered Riemann surfaces. In the semi-classical limit these microstates can be counted using intersection theory on the moduli space of punctured Riemann surfaces. We make a conjecture (supported by numerics) for the asymptotic behaviour of the relevant intersection numbers. The result is that the geometric microstates with fixed topology have an entropy which grows too slowly t…
We study extremal static dyonic black holes in four-dimensional Einstein-Maxwell-Dilaton theory, for general values of the constant $a$ in the exponential coupling $e^{aϕ}$ of the dilaton to the Maxwell kinetic term. Explicit solutions are known only for $a=0$, $a=1$ and $a=\sqrt3$, and for general $a$ when the electric and magnetic charges $Q$ and $P$ are equal. We obtain solutions as power series expansions around $Q=P$, in terms of a small parameter $ε= a^{-1}\, \log(Q/P)$. Using these, and also solutions constructed numerically, we test a relation between the mass and the charges that had …
Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole. The latter statement can be interpreted in two ways. First, at the fully non-perturbative level of AdS/CFT at finite N, it means that cluster decomposition does not hold in the bulk. This may be viewed as a sharp manifestation of the bulk non-locality a…
Light probes interacting with heavy bound states such as black holes give rise to interesting observables containing valuable dynamical information. Recently, a family of black hole microstates was shown to admit an exact string worldsheet description. We construct the physical vertex operators of these models, and derive their form in the low-energy AdS$_3$ limit. We then compute an extensive set of novel heavy-light correlators in these backgrounds. A subset of these provide the first match between worldsheet correlators in black hole microstates and the holographically dual conformal field …
We present a sample microstate for a black ring in four and five dimensional language. The microstate consists of a black string microstate with an additional D6-brane. We show that with an appropriate choice of parameters the piece involving the black string microstate falls down a long AdS throat, whose M-theory lift is AdS_3 X S^2. We wrap a spinning dipole M2-brane on the S^2 in the probe approximation. In IIA, this corresponds to a dielectric D2-brane carrying only D0-charge. We conjecture this is the first approximation to a cloud of D0-branes blowing up due to their non-abelian degrees …
This work studies dynamics controlling the transition between different microstates of two charge D1-D5 black holes by network methods, in which microstates of the system are defined as network nodes, while transitions between them are defined as edges. It is found that the eigenspectrum of this network's Laplacian matrix, which is identified with Hamiltonians of the microstate system, has completely the same Nearest-Neighbor Spacing Distribution as that of general Gaussian Orthogonal Ensemble of Random Matrices. According to the BGS, i.e. Bohigas, Giannoni and Schmit conjecture, this forms ev…
We investigate the possibility that the geometry dual to a typical AdS black hole microstate corresponds to the extended AdS-Schwarzschild geometry, including a region spacelike to the exterior. We argue that this region can be described by the mirror operators, a set of state-dependent operators in the dual CFT. We probe the geometry of a typical state by considering state-dependent deformations of the CFT Hamiltonian, which have an interpretation as a one-sided analogue of the Gao-Jafferis-Wall traversable wormhole protocol for typical states. We argue that the validity of the conjectured bu…
We argue that the fundamental "atomic objects" in string theory are themelia: extended objects that have 16 supersymmetries locally. We show that all existing smooth horizonless microstate geometries can be seen as bound states of themelia, and we conjecture that all such bound states with suitable KKM charges will give rise to microstate geometries. We also construct the most general themelion with a three-torus isometry and show that it interpolates between superstrata and the super-maze.
We argue that the region behind the horizon of a one-sided black hole can be probed by an analogue of the double-trace deformation protocol of Gao-Jafferis-Wall. This is achieved via a deformation of the CFT Hamiltonian by a term of the form ${\cal O} \widetilde{\cal O}$, where $\widetilde{\cal O}$ denote the state-dependent "mirror operators". We argue that this deformation creates negative energy shockwaves in the bulk, which allow particles inside the horizon to escape and to get directly detected in the CFT. This provides evidence for the smoothness of the horizon of black holes dual to ty…
Four-dimensional supersymmetric black holes are static and so have all vanishing multipoles. Nevertheless, it is possible to define finite multipole ratios for these black holes, by taking the ratio of (finite) multipoles of supersymmetric multicentered geometries and then taking the black hole scaling limit of the multipole ratios within these geometries. An alternative way to calculate these multipole ratios is to deform the supersymmetric black hole slightly into a non-extremal, rotating black hole, calculate the multipole ratios of this altered black hole, and then take the supersymmetric …
Multi-centered bubbling solutions are black hole microstate geometries that arise as smooth solutions of 5-dimensional $\mathcal{N}=2$ Supergravity. When these solutions reach the scaling limit, their resulting geometries develop an infinitely deep throat and look arbitrarily close to a black hole geometry. We depict a connection between the scaling limit in the moduli space of Microstate Geometries and the Swampland Distance Conjecture. The naive extension of the Distance Conjecture implies that the distance in moduli space between a reference point and a point approaching the scaling limit i…
This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory. To this aim, important ingredients are holography and supersymmetric localization. Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on $Σ_\mathfrak{g} \times T^{n}$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory. This defines…
We construct smooth BPS three-charge geometries that resolve the zero-entropy singularity of the U(1) x U(1) invariant black ring. This singularity is resolved by a geometric transition that results in geometries without any branes sources or singularities but with non-trivial topology. These geometries are both ground states of the black ring, and non-trivial microstates of the D1-D5-P system. We also find the form of the geometries that result from the geometric transition of N zero-entropy black rings, and argue that, in general, such geometries give a very large number of smooth bound-stat…
We extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evapo…
In the LLM bubbling geometries, we compute the entropies of black holes and estimate their "horizon" sizes from the fuzzball conjecture, based on coarse-graining on the gravity side. The differences of black hole microstates cannot be seen by classical observations. Conversely, by counting the possible deformations of the geometry which are not classically detectable, we can calculate the entropy. We carry out this method on the black holes of the LLM bubbling geometries, such as the superstar, and obtain the same result as was derived by coarse-graining directly on the CFT (fermion) side. Sec…
Attempts to find black hole microstates using the Hamiltonian phase space approach have been made on the Schwarzschild spacetime. Since the Schwarzschild spacetime is also in the larger family of the Kerr spacetimes, and both are asymptotically flat, the Kerr black hole is a good option for the method development. The Kerr black hole is a spinning one. We perform this analysis on the Kerr spacetime and we obtain promising results using the covariant phase space analysis. Although we have forced ourselves to use the Bondi fall-off conditions, we find the gauge degrees of freedom that could be g…
Recent studies of asymptotic symmetries suggest, that a Hamiltonian phase space analysis in gravitational theories might be able to account for black hole microstates. In this context we explain, why the use of conventional Bondi fall-off conditions for the gravitational field is too restrictive in the presence of an event horizon. This implies an enhancement of physical degrees of freedom ($\mathcal{A}$-modes). They provide new gravitational hair and are responsible for black hole microstates. Using covariant phase space methods, for the example of a Schwarzschild black hole, we give a propos…
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-d…
For extremal black holes the fuzzball conjecture says that the throat of the geometry ends in a quantum `fuzz', instead of being infinite in length with a horizon at the end. For the D1-D5 system we consider a family of sub-ensembles of states, and find that in each case the boundary area of the fuzzball satisfies a Bekenstein type relation with the entropy enclosed. We suggest a relation between the `capped throat' structure of microstate geometries and the fact that the extremal hole was found to have zero entropy in some gravity computations. We examine quantum corrections including string …
Supersymmetric black holes provide an excellent theoretical laboratory to test ideas about quantum gravity in general and black hole entropy in particular. When four-dimensional supergravity is interpreted as the low-energy approximation of ten-dimensional string theory or eleven-dimensional M-theory, one has a microscopic description of the black hole which allows one to count microstates and to compare the result to the macroscopic (geometrical) entropy. Recently it has been conjectured that there is a very direct connection between the partition function of the topological string and a part…
We propose a program for counting microstates of four-dimensional BPS black holes in N >= 2 supergravities with symmetric-space valued scalars by exploiting the symmetries of timelike reduction to three dimensions. Inspired by the equivalence between the four dimensional attractor flow and geodesic flow on the three-dimensional scalar manifold, we radially quantize stationary, spherically symmetric BPS geometries. Connections between the topological string amplitude, attractor wave function, the Ooguri-Strominger-Vafa conjecture and the theory of automorphic forms suggest that black hole degen…
We comment on a recent paper of Almheiri, Marolf, Polchinski and Sully who argue against black hole complementarity based on the claim that an infalling observer 'burns' as he approaches the horizon. We show that in fact measurements made by an infalling observer outside the horizon are statistically identical for the cases of vacuum at the horizon and radiation emerging from a stretched horizon. This forces us to follow the dynamics all the way to the horizon, where we need to know the details of Planck scale physics. We note that in string theory the fuzzball structure of microstates does no…
Extreme and very-near-extreme spin J Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges c_L=c_R=12J. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic non-extreme values of the mass M. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The periodic identification of the azimuthal angle is shown to correspond to a spontaneous brea…
Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area…
The aim of this paper is to elucidate a close connection between the black hole area law and the infinite distance conjecture in the context of the swampland. We consider families of black hole geometries, parametrized by their event horizon areas or by the values of their entropies, and show that the infinite entropy limit is always at infinite distance in the space of black hole geometries. It then follows from the infinite distance conjecture that there must be a tower of states in the infinite entropy limit, and that ignoring these towers on the horizon of the black hole would invalidate t…
We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi-Yau compactifications. This quantum mechanics describes the dynamics of D-branes in the near-horizon attractor geometry of the black hole. In many cases, the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. Both the attractor mechanism and notions of marginal stability play important roles in generating the large number of microstates required to explain this entropy. We compute the microscopic entropy explicitly in a few different cases, where …
We derive a universal formula for the asymptotic growth of the mean value of three-point coefficient for Warped Conformal Field Theories (WCFTs), and provide a holographic calculation in BTZ black holes. WCFTs are two dimensional quantum field theories featuring a chiral Virasoro and U(1) Kac-Moody algebra, and are conjectured to be holographically dual to quantum gravity on asymptotically AdS$_3$ spacetime with Comp$\grave{\mathrm{e}}$re-Song-Strominger boundary conditions. The WCFT calculation amounts to the calculation of one-point functions on torus, whose high temperature limit can be app…
We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times Σ$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $Σ$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetri…
We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) action…
To model the interior of a black hole, a study is made of a spin system with long-range random four-spin couplings that exhibits quantum chaos. The black hole limit corresponds to a system where the microstates are approximately degenerate and equally likely, corresponding to the high temperature limit of the spin system. At the leading level of approximation, reconstruction of bulk physics implies that local probes of the black hole should exhibit free propagation and unitary local evolution. We test the conjecture that a particular mean field Hamiltonian provides such a local bulk Hamiltonia…
We study microscopic operators describing the experience of an observer falling into the horizon of a unitarily evaporating black hole. For a young black hole, these operators can be taken to act only on the degrees of freedom in the black hole region: the soft---or stretched horizon---modes as well as the semiclassical modes in the zone region. On the other hand, for an old black hole, the operators must also involve radiation emitted earlier; the difference between the two cases comes from statistics associated with the coarse-graining performed to obtain the effective theory of the interior…
The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome `remnants'. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta i…
The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, arXiv:0810.4301. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the `chromosomes' of a D-particle or a black hole. As polar st…
If the evaporation of a black hole formed from a pure state is unitary, the entanglement entropy of the Hawking radiation should follow the Page curve, increasing from zero until near the halfway point of the evaporation, and then decreasing back to zero. The general argument for the Page curve is based on the assumption that the quantum state of the black hole plus radiation during the evaporation process is typical. In this paper, we show that the Page curve can result from a simple dynamical input in the evolution of the black hole, based on a recently proposed signature of quantum chaos, w…
The large $N$ limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS$_5$ black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large $N$ with arbitrary chemical potentials for all charges and angular momenta, for general $\mathcal{N}=1$ four-dimensional conformal theories with a holographic dual. We conjecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large $N$. For $\mathcal{N}=4$ S…
